Defining parameters
Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 600.bt (of order \(20\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 100 \) |
Character field: | \(\Q(\zeta_{20})\) | ||
Newform subspaces: | \( 0 \) | ||
Sturm bound: | \(480\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(600, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2944 | 0 | 2944 |
Cusp forms | 2816 | 0 | 2816 |
Eisenstein series | 128 | 0 | 128 |
Decomposition of \(S_{4}^{\mathrm{old}}(600, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(600, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)